1. Field of the Invention
The invention relates to digital analysing and synthesizing filter banks.
2. Description of the Related Art
Digital filter banks can be used for spectrally dividing an incoming digital input signal into sub-band signals, more specifically during the transmission, storage and processing of the signals. Depending on the application, the sub-band signals thus produced are encoded and/or processed. Because of the reduced bandwidth of the digital sub-band signals produced by means of a digital filter bank, the sub-band signals can be represented by samples having a reduced sampling rate in accordance with the conventional sampling theorem. As a result, both the computational cost and efforts for the analysing filter bank and the cost and efforts for the transmission, storage or other processing of the sub-band signals can be reduced correspondingly.
Because of the sampling rate reduction effected in the analysing filter bank it is necessary for the reconstruction or synthesis of an output signal from the processed sub-band signals to increase the sampling rate in a synthesizing filter bank. By increasing the sampling frequency to the original value an interpolation of the sub-band signals is effected and the interpolated sub-band signals thus obtained are additively combined to produce the output signal.
As mentioned already in the foregoing, in order to reduce the cost and efforts, particularly in the transmission and storage of signals, it is necessary to effect a maximum sampling rate reduction. The maximum sampling rate reduction is obtained in accordance with the sampling theorem from the bandwidth of the sub-band signals. For the assumed case of a digital filter bank having channels of a constant bandwidth Fa/M, Fa designating the sampling rate of the input signals and M the number of the channels, the sampling rate can be reduced by a factor r=M/2 for real band filters or, when it is assumed that the band filters are ideal filters, it can be reduced by a factor r=M for complex band filters. Because of the finite edge steepness of real filters, however, the above-mentioned maximum sampling rate reduction cannot be realised.
The book "Multirate Digital Signal Processing" by Ronald E. Crochiere, Prentice-Hall, Inc., Englewood Cliffs, N.J. 07632, more specifically pages 376 to 382, discloses for the special case M=2 and r=2 a solution, known as quadrature mirror filtering (QMF), in which the occurring spectral folding (aliasing) components are compensated for in the synthesizing filter bank. By interconnecting a total of (M-1) two-channel filter banks to form a tree structure, a maximum sampling rate reduction can also be effected for an M-channel filter bank (cf. page 379).
The M-channel filter bank thus obtained has the disadvantage that on the one hand a comparatively high cost and effort is required for the in total 2(M-1) filters, and on the other hand, that the cascade arrangement of log.sub.2 (M) sub-filters in each tree branch involves a large signal delay.
For filter banks having a number of channels M&gt;2 which do not operate with a maximum sampling rate reduction, a polyphase filter bank is often used which, as compared with the above-mentioned tree structure, requires a lower circuit cost and design effort. The published German patent application DE-OS 31 18 473, corresponding to U.S. Pat. No. 4,623,980, discloses a multi-channel filter bank which is constituted by the combination of a digital polyphase network with a processor performing a discrete Fourier transform (DFT). This filter bank has a significantly shorter signal delay as compared with the filter bank having a tree structure and, in addition, the circuit cost and design effort is less.
However, in the case in which a maximum sampling rate reduction is effected, aliasing distortions occur in the above-mentioned filter bank which are not compensated for in the synthesizing filter bank.